Transient macroscopic quantum superposition states in degenerate parametric oscillation: Calculations in the large-quantum-noise limit using the positivePrepresentation

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Abstract
Recent work by Wolinsky and Carmichael $[—OSA Annual Meeting, 1989 Technical Digest Series Vol. 18 (Optical Society of America, Washington, DC, 1989)] suggests that a superposition of two macroscopically distinct coherent states (a ‘‘Schrödinger-cat’’ state) may be produced in degenerate parametric oscillation in a transient regime. We investigate this possibility by performing numerical simulations of quantum stochastic equations derived using the positive P representation. The equations allow for finite signal cavity loss. Interference fringes which indicate the existence of the macroscopic superposition states are indeed predicted in regimes where the parametric nonlinearity is sufficiently large compared to the signal cavity losses. Experimental criteria needed for the generation of macroscopic quantum superposition states using parametric oscillation are thus established.